Frequency and temperature compensation synthesis for a MEMS resonator

ABSTRACT

Disclosed herein is a signal generation technique based on a reference frequency provided by a MEMS resonator. The signal generation technique compensates for temperature- and fabrication process-induced frequency variations collectively. In some embodiments, a device implementing the disclosed signal generation technique includes a fractional-N synthesizer, a temperature sensor, calibration data, and a sigma-delta modulator to adjust the reference frequency of the MEMS resonator to a desired frequency value while compensating for the temperature variation of the MEMS resonator.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims the benefit of U.S. provisional application Ser.No. 60/677,288, filed May 3, 2005, and entitled “Frequency andTemperature Compensated MEMS Resonator,” the entire disclosure of whichis hereby expressly incorporated by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under Contract No.:70NANB4H3001 awarded by the National Institute for Standards andTechnology (NIST). The government has certain rights in the invention.

This application relates to commonly assigned and concurrently filedU.S. non-provisional application entitled “MEMS Resonator-Based SignalModulation” Ser. No 11/417,833, the entire disclosure of which is herebyexpressly incorporated by reference.

BACKGROUND OF THE DISCLOSURE

1. Field of the Disclosure

The disclosure relates generally to frequency synthesis devices and,more particularly, to frequency synthesis using MEMS(microelectromechanical systems) resonators, or microresonators, forreference signal generation.

2. Brief Description of Related Technology

MEMS resonators are attractive for use in many applications as acost-effective replacement for discrete devices such as quartz crystaloscillators or surface-acoustic wave (SAW) resonators. MEMS resonatorsare particularly promising for use in wireless communications systems,as they can be fabricated alone or on substrates with other circuitry,such as MOS or bipolar circuits. MEMS resonators can also have very highmechanical quality factors (Q), which leads to good frequencyselectivity. MEMS resonators also typically consume less power thantheir discrete counterparts.

MEMS resonators are not without drawbacks, however. The center frequencyof a MEMS resonator is determined by its physical characteristics, whichare, in turn, functions of design, materials, and the processing methodsused to fabricate the resonator. Due to its high-Q nature and the normalprocess variations that occur in fabrication, it is difficult tofabricate a MEMS resonator with a center frequency accuracy of betterthan a few percent.

Many applications for which MEMS resonators are well suited demandinitial accuracy of between 1 and 100 parts-per-million (ppm), which is3 to 5 orders of magnitude more precise than typical accuracy. In orderto reach the requisite level of accuracy, laser trimming or othermethods have been used. Trimming methods have generally been found toundesirably add to the complexity and cost of the fabrication process.Thus, despite the number of different trimming methods available, itwould nonetheless be desirable to develop an alternative for achievingthe necessary 1 to 100 ppm center-frequency accuracy that does notinvolve trimming and other complex fabrication steps.

In addition to initial frequency inaccuracy, the resonant frequency of aMEMS resonator is dependent on temperature. The temperature dependencyof the resonant frequency can be as much as 17 ppm/° C. Unfortunately,the maximum allowable temperature variation is 0.02 to 1 ppm/° C. (adifference of 4 orders of magnitude) for many applications. Severalmethods for achieving temperature compensated MEMS resonator structureshave been proposed, but these proposals have all required additionalprocessing steps during resonator fabrication. The cost and complexityadded by these processing steps make these approaches unattractive.

A method of adjusting the initial frequency of a MEMS resonator andcompensating for temperature-change-induced frequency variation withoutthe need for extra manufacturing steps during fabrication would bedesirable. Such a method would reduce the cost and manufacturingcomplexity associated with producing a MEMS resonator product.

SUMMARY OF THE DISCLOSURE

Disclosed herein is an apparatus that generates a signal based on thefrequency developed by a MEMS resonator and compensates for anytemperature-induced frequency variation without some of the costs anddisadvantages in the prior art. In some embodiments, the apparatusincludes a MEMS resonator and synthesizer circuitry. The synthesizercircuitry is responsive to a temperature sensor and calibration data todevelop an output signal having a desired frequency. To that end, theapparatus may include a fractional-N synthesizer and a sigma-deltamodulator to compensate for the temperature variation of the MEMSresonator.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

For a more complete understanding of the disclosure, reference should bemade to the following detailed description and accompanying drawingfigures, in which like reference numerals identify like elements in thefigures, and in which:

FIG. 1 is a block diagram of a MEMS-based signal generation device inaccordance with one aspect of the disclosure;

FIG. 2 is a block diagram of a frequency synthesizer circuit of thesignal generation device of FIG. 1 in accordance with an exemplaryembodiment; and,

FIG. 3 is a block diagram of a frequency synthesizer circuit of thesignal generation device of FIG. 1 in accordance with another exemplaryembodiment.

While the disclosed devices and methods are susceptible of embodimentsin various forms, there are illustrated in the drawing (and willhereafter be described) specific embodiments of the invention, with theunderstanding that the disclosure is intended to be illustrative, and isnot intended to limit the invention to the specific embodimentsdescribed and illustrated herein.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The invention generally relates to a frequency compensation techniquefor MEMS resonators that addresses multiple contributions to frequencyvariance from a variety of sources, including temperature-inducedfrequency changes and fabrication process-based frequency offsets. Thedisclosed technique includes and involves the generation of a compositecompensation factor that accumulates or combines the multiple frequencyvariance contributions to control the synthesis of an output signalhaving a compensated frequency. In this way, any offsets or variances inthe reference frequency developed by the MEMS resonator are addressedcollectively.

Generally speaking, the composite compensation factor achieves frequencycompensation via adjustment (or re-calculation) of the frequencydivision factors for the frequency synthesis in accordance therewith.

FIG. 1 depicts an exemplary signal generation device indicated generallyat 100 configured to implement the disclosed frequency and temperaturecompensation technique in accordance with one embodiment. The device 100generates a frequency compensated output signal from a reference signalprovided by a MEMS resonator 102 via an input port or line 103. Thefrequency of the reference signal is adjusted in accordance with acontrol signal provided by a processor 104 via an input port or line105. The output signal is generated by synthesizer circuitry 106 fromthe reference signal in accordance with the control signal. In somecases, the circuitry 106 may implement fractional-N synthesis, as shownin the exemplary embodiment of FIG. 1 and described below. Moregenerally, the synthesizer circuitry 106 implements any desiredfrequency multiplication scheme to arrive at the frequency of the outputsignal. To that end, the circuitry 106 may include a frequencymultiplier (and frequency divider) to generate the output signal on anoutput line 107 based on the reference frequency of the MEMS resonator102 and the control signal from the processor 104.

The signal generation device 100 is programmable in the sense that thecontrol signal may include and provide a digital representation of adesired frequency for the output signal. The synthesizer circuitry 106is responsive to the digital representation to adjust the frequency ofthe output signal accordingly. For example, the MEMS resonator 102 mayprovide a frequency of 80 MHz to the synthesizer circuitry 106. Theoutput signal generated via the synthesizer circuitry 106 may have anoutput frequency of 250 MHz. In some embodiments, the synthesizercircuitry 106 includes a fractional-N synthesizer to tune the initialfrequency and compensate for frequency variations due to temperaturechanges of MEMS resonator 102 in a rapid manner. Alternatively, aninteger synthesizer may be used. The trimming accuracy of an integer-Nsynthesizer is determined by a comparison source frequency. For example,in order to achieve a 10 ppm trimming accuracy (as required in manyapplications) for an output frequency of 250 MHz, an integer-Nsynthesizer would require a comparison frequency of 2.5 KHz. As aresult, associated lock-time for the synthesizer can become prohibitive.The trimming accuracy of a fractional-N synthesizer, on the other hand,can be very small—even when maintaining a high comparison frequency anda wide loop bandwidth; therefore, lock time is reduced.

In the foregoing example, the ratio of the output frequency to thecomparison frequency is 10⁵, which adds 90 dB to a phase detector noisefloor typically around −150 dBc/Hz, resulting in a loop phase noise of−50 dBc/Hz. In the case of the device 100, the achievable in-loop phasenoise is that of the reference plus the ratio of the output frequency tothe reference frequency, or approximately 10 dB. MEMS resonator 102 hasa 1 KHz phase noise of −115 dBc/Hz, which results in an in-loop phasenoise of −105 dBc/Hz. It will be clear to those skilled in the art thatthe phase noise characteristics of the MEMS resonator 102 and thesynthesizer circuitry 106 are merely exemplary, and that otherphase-noise characteristics are possible without departing from thescope of the present invention.

FIG. 2 depicts the synthesizer circuitry 106 in greater detail and inaccordance with an exemplary embodiment. The synthesizer circuitry 106may be implemented via one or more integrated circuits, such as, forexample, a single application-specific integrated circuit, or ASIC. Thesynthesizer circuitry 106 includes a temperature sensor 210 to monitorthe temperature at which the MEMS resonator 102 operates. The MEMSresonator 102 is characteristic of most MEMS resonators, in that it hasa linear temperature characteristic over a very wide temperature range.Therefore, a piecewise linear temperature characteristic may be used forcalibration purposes, as described below. An A/D converter 212 convertsthe output of the temperature sensor 210 to digital information, whichis then relayed to a temperature register 214. The initial frequency(i.e., the resonant frequency of as-fabricated MEMS resonator 102) iscalibrated at manufacturing and the value is stored in initial frequencycalibration register 216 (hereinafter, ROM 216). The value stored in theROM 216 and the value stored in the temperature register 214 are addedto the value stored in a desired frequency register 218 by an adder 220and relayed to a sigma-delta fractional synthesizer 222. Although theembodiment presented utilizes a sigma-delta fractional synthesizer, itwill be clear to those skilled in the art, after reading thisspecification, how to make and use alternative embodiments of thepresent invention that utilize any type of synthesizer.

The output of the sigma-delta fractional synthesizer 222 is relayed to aloop filter 224, which then provides an input to a VCO 226. The outputof the VCO 226 provides the output signal on the line 107 (FIG. 1) ofthe signal generation device 100.

Although the embodiment described above utilizes a fractional-Nsynthesizer comprising a sigma-delta modulator, other types ofsynthesizers, such as integer synthesizers, may be used alternatively oradditionally.

FIG. 3 depicts an alternative embodiment in which the respectivecontributions to the frequency variance or offset are compiled andaddressed collectively via a composite frequency compensation parameter.The composite parameter is generally determined from data derived fromthe frequency of the MEMS resonator reference signal, the operatingtemperature for the MEMS resonator, and the desired output signalfrequency.

In the exemplary embodiment shown in FIG. 3, a signal generation device300 receives a resonator signal from a MEMS resonator 302 via an inputport 304. An indication of the operating temperature for the MEMSresonator 302 is provided by a temperature sensor 306, which may beintegrated with the rest of the circuitry of the signal generationdevice 300 as an on-chip sensor, or received via an input port ifdisposed externally. An indication of a desired output frequency isprovided via an input port 310. In this way, the device 300 may beprogrammed by an external source that develops a control signal for thedesired frequency. The external source may also provide an activationsignal to enable operation of the device 300.

The device 300 includes an oscillator circuit 312 to amplify, conditionand facilitate oscillation of the resonator signal, which is then passedto a regulator 314 prior to processing by a phase-lock loop circuit. Thephase-lock loop circuit includes a phase and frequency detector 316, acharge pump 318, a loop filter indicated generally at 320, and a VCO322. The phase-lock the circuit further includes a programmable divider324 responsive to, or controlled by, a division factor generated by afractional-n synthesizer 326 having a sigma-delta modulator 328.

In operation, the programmable divider 324 supports the frequencymultiplication provided by the phase-lock loop circuit involved ingenerating the desired output frequency from the resonator signal.Furthermore, the programmable divider 324 and the fractional-nsynthesizer 326 implement frequency compensation for the MEMS resonator302 based on input parameters provided by a controller or control system330. Generally speaking, the controller 330 compiles the effects of boththe operating temperature and process fabrication to generate asynthesizer control signal provided to the fractional-n synthesizer 326.The control signal may include one or more synthesizer input parameters,such as the division factors N and F. Modified versions of thesedivision factors are derived from a composite frequency compensationparameter calculated by a control logic 332 implemented by thecontroller 330. The control logic 332 may be responsive to data storedin one or more registers 334 and other memories, such as a ROM or PROM336. Generally speaking, the data stored in the memories 334, 336 may beindicative of calibration data associated with the MEMS resonator 302.For example, an initial output frequency for the MEMS resonator 302 maybe stored, as well as a temperature characteristic.

The controller 330 may receive data indicative of the operatingtemperature from an analog to digital converter (ADC) 338 incommunication with the temperature sensor 306. The ADC 338 may have highresolution and accuracy to accommodate temperature sensing as accurateas 0.1 C over a temperature range of, for instance, −50 C to 150 C.Dividing that temperature range at that resolution results in an 11 bitADC for the temperature sensor 306.

Despite the high resolution and accuracy of the temperature indication,the temperature characteristic utilized by the control logic 332 neednot be based on many actual data points for the MEMS resonator 302.Rather, in some embodiments, the temperature characteristic may bederived from as few as three data points. From those points, a piecewiselinear characteristic may be generated as described below.

The temperature characteristic is one of many components to thedetermination of the composite frequency compensation parameter. Furtherdetails regarding the determination are provided below. Generallyspeaking, however, the composite frequency compensation parameter isused to control the fractional-n synthesizer 326 and thereby control thefrequency multiplication implemented by the device 300 such that afterprocessing by a post scaler 340 and an output driver 342, an outputsignal is developed or generated on an output line 344.

Temperature and Process Compensation.

The control logic shown in FIG. 3 may implement the exemplarytemperature compensation algorithm described below. The objective of thealgorithm is to modify the synthesizer division factor to correct forresonator frequency shifts due to both fabrication process andtemperature. This collective approach to frequency synthesis may beachieved by calibrating the resonator and synthesizer together atseveral temperatures to determine a linear (or piecewise linear)characteristic of the resonator frequency as a function of thetemperature.

Because the resonator may have a process spread in its resonancefrequency of ±5% in addition to a temperature coefficient of TC˜−20ppm/C, the output frequency may vary significantly. The output frequencyf_(out) (FIG. 3) is determined by the resonator frequency f_(Xtal) andthe PLL division factors N, F, R and M through the following equation:

${fout} = \frac{{fXtal} \cdot \left( {N + {F/2^{f}}} \right)}{R \cdot M}$

As shown below, one way to address and compensate for any error in theoutput frequency due to a change in fXtal is by modifying the factors Nand F (i.e., to NP and FP) such that the error between the actual outputfrequency and the required frequency is better than a desired threshold,such as ±10 ppm:

${fout}_{Error\_ ppm} = {\frac{{fout}_{act} - {fout}_{req}}{{fout}_{req}}\underset{\_}{<}{{\underset{\_}{+}10}{ppm}}}$

In accordance with one embodiment, the modified factors NP and FP may bedetermined using the following algorithm based on a compositecompensation parameter, K_PT that combines the effects of both processvariation and temperature-induced variation:

$\begin{matrix}{{{NP} + \frac{FP}{2^{f}}} = {\left( {N + \frac{F}{2^{f}}} \right) \cdot \left( {1 - {K\_ PT}} \right)}} \\{{K\_ PT} = \frac{{\Delta\;{fXtal}_{proc}} + {\Delta\;{{fXtal}_{T} \cdot \left( {T - T_{nom}} \right)}}}{{fXtal}_{0{\_ nom}} + {\Delta\;{fXtal}_{proc}} + {\Delta\;{{fXtal}_{T} \cdot \left( {T - T_{nom}} \right)}}}}\end{matrix}$ΔfXtal _(proc) =fXtal _(nom) −fXtal ₀ _(—) _(nom)ΔfXtal _(T) =Xftal _(nom) ·TC

As shown in FIG. 3, a temperature measurement may be provided via atemperature sensor or system including, for instance, a PTAT temperaturesensor and an 11-bit A/D converter used to provide a digitalrepresentation of the temperature of the resonator. In some embodiments,the algorithm determines K_PT using a two-segment piecewise linearapproximation. The 11-bit reading of the A/D converter (adc) will beused to calculate K_PT, which, in turn, is used to calculate NP and FP.The Sigma-Delta Modulator is then given NP and FP as its inputs ratherthan the inputs originally stored in the Register File N and F.

An exemplary temperature compensation algorithm is based on athree-point calibration technique that uses a two segment approximationof K_PT as a function of adc. The following procedure may be utilized tocalibrate the system:

1. Power-Up Chip and load defaults.

2. Load calibration division factor (N=32, F=0, M=24, R=2), turn OFFTemp. Comp Algorithm. Required frequency is fXtal0_nom=19.0 MHz

3. Change chip temperature to target

4. Measure o/p frequency and compare with required frequency

5. Calculate (OFF chip) required N′ and F′ to correct frequency using:

${Ntot} = {{N^{\prime} + \frac{F^{\prime}}{2^{16}}} = \frac{32 \cdot {fXtal}_{0{\_ nom}}}{{fout}_{meas}}}$N′=fix(Ntot)F′=round((N′−Ntot)·2¹⁶)

6. Load calculated N′ and F′ to registers of N and F

7. Measure o/p frequency and compare with required frequency, iferror >0.5 ppm repeat procedures (5) & (6).

8. Calculate K_PT (OFF chip) using:

${K\_ PT} = \frac{\left( {N^{\prime} - 32} \right) + {F^{\prime}/2^{16}}}{32}$

9. Load K_PT and store in SRAM (SRAM is not Register File rather memoryavailable in PPROM).

10. Write A/D o/p (adc) to OUTP port and check if in range

11. Store ADC output in SRAM

12. Keep supply ON and change temperature, procedure (3). Repeat tocover 3 points.

13. Calculate slopes m1 and m2 externally using stored (adc, K_PT)stored points in SRAM:

$\begin{matrix}{{m\; 1} = \frac{{{K\_ PT}(1)} - {{K\_ PT}(2)}}{{{adc}(1)} - {{adc}(2)}}} \\{{m\; 2} = \frac{{{K\_ PT}(3)} - {{K\_ PT}(2)}}{{{adc}(3)} - {{adc}(2)}}}\end{matrix}$

14. Load m1, m2 and reference point (point 2) to Register Map

15. Enable Temperature Compensation and measure output frequency tocheck for ppm error <10 ppm

16. Fuse PPROM

The required error may be achieved using a 16-bit sigma-delta modulatorand an 11-bit ADC, although other sizes may also be sufficient. Thecalculations may be performed internally digitally using memoriescapable of handling the following representations for the parametersK_PT, adc and m:

N: 6 bits

F: 16 bits

adc: 11 bits

K_PT: 20 bits 2's complement format after scaling by 219

m1, m2: 8 bits after scaling by 228 and taking absolute value

In some applications, the output signal may be indicative of analoginformation or digital data via frequency modulation or frequency-shiftkeying encoding, as described in the above-referenced, concurrentlyfiled patent application. In such cases, the above-describedcompensation technique may be useful to ensure that temperature andother effects do not distort the transmission of data or information viafrequency drift. Generally speaking, the reference frequency developedby the MEMS resonator may reflect the information or data to betransmitted. A description of the manner in which the referencefrequency (i.e., the resonant frequency of the MEMS resonator) may bemodulated is set forth in the above-referenced patent application.

Embodiments of the disclosed system and method may be implemented inhardware, software, firmware or any combination thereof. Someembodiments may be implemented with computer programs executing onprogrammable systems having at least one processor, a data storagesystem (including volatile and non-volatile memory and/or storageelements), at least one input device, and at least one output device.The programs may be implemented in a high level procedural or objectoriented programming language to communicate with a processing system.The programs may also be implemented in assembly or machine language, ifdesired. In fact, practice of the disclosed system and method is notlimited to any particular programming language. In any case, thelanguage may be a compiled or interpreted language.

While the present invention has been described with reference tospecific examples, which are intended to be illustrative only and not tobe limiting of the invention, it will be apparent to those of ordinaryskill in the art that changes, additions and/or deletions may be made tothe disclosed embodiments without departing from the spirit and scope ofthe invention.

The foregoing description is given for clearness of understanding only,and no unnecessary limitations should be understood therefrom, asmodifications within the scope of the invention may be apparent to thosehaving ordinary skill in the art.

1. A device for generation of an output signal having a desiredfrequency, the device comprising: a MEMS resonator to generate areference signal; a frequency synthesizer to develop the output signalfrom the reference signal; a temperature sensor to generate an analogindication of an operating temperature for the MEMS resonator; ananalog-to-digital converter to develop a digital representation of theoperating temperature from the analog indication thereof, the digitalrepresentation having a resolution of at least 11 bits; and, acontroller to compile frequency compensation contributions from thedigital representation of the operating temperature and a digitalindication of the desired frequency to generate a synthesizer controlsignal provided to the frequency synthesizer.
 2. The device of claim 1,wherein the controller determines the frequency compensationcontribution from the digital representation of the operatingtemperature based on a linear temperature characteristic for the MEMSresonator.
 3. The device of claim 1, wherein the controller iscalibrated to generate the synthesizer control signal from a compositecompensation factor based on a linear function of the digitalrepresentation of the operating temperature.
 4. The device of claim 3,wherein the linear function comprises a pair of linear segments about areference point.
 5. The device of claim 4, wherein the controller iscalibrated with data indicative of respective slopes of the pair oflinear segments.
 6. The device of claim 3, wherein the linear functionis a piecewise linear approximation.
 7. The device of claim 3, whereinthe analog-to-digital converter is configured to develop the digitalrepresentation of the operating temperature within an accuracy of 0.1 C.8. The device of claim 3, wherein the synthesizer control signalcomprises phase-locked loop (PLL) division factors for the frequencysynthesizer.
 9. The device of claim 3, wherein the linear function isfurther based on an initial frequency offset of the MEMS resonator fromthe desired frequency.
 10. The device of claim 9, wherein the controllercomprises a memory in which data indicative of the linear function isstored, the data comprising multiple slope parameters and a referencepoint.
 11. A method of frequency compensation for a desired outputfrequency in connection with a MEMS resonator, the method comprising thesteps of: receiving a resonator signal from the MEMS resonator;providing a temperature signal indicative of an operating temperaturefor the MEMS resonator; determining a composite frequency compensationparameter in accordance with multiple slope quantities for a piecewiselinear approximation based on the temperature signal and the desiredoutput frequency; and, generating an output signal having the desiredoutput frequency using a frequency synthesizer based on the compositefrequency compensation parameter; wherein the providing step comprisesthe step of converting the temperature signal from an analogrepresentation of the operating temperature into a digitalrepresentation of the operating temperature; and wherein the convertingstep is performed such that the digital representation of the operatingtemperature is within an accuracy of 0.1 C.
 12. The method of claim 11,wherein the piecewise linear approximation is a function of theoperating temperature.
 13. The method of claim 12, wherein thegenerating step comprises the step of developing a synthesizer controlsignal from the composite frequency compensation parameter.
 14. Themethod of claim 13, wherein the synthesizer control signal comprisesdata indicative of phase-locked loop (PLL) division factors.
 15. Themethod of claim 12, wherein the piecewise linear approximation isfurther based on an initial frequency offset of the MEMS resonator fromthe desired output frequency.
 16. A device to generate an output signalhaving a desired frequency in connection with a MEMS resonator, thedevice comprising: an analog-to-digital converter to develop a digitalrepresentation of an operating temperature for the MEMS resonator; acontroller to generate a control signal based on the digitalrepresentation of the operating temperature, the controller comprising amemory and control logic, wherein the memory stores data comprisingmultiple slope quantities for a piecewise linear approximation of acomposite frequency compensation factor, and wherein the control logicis configured to determine the composite frequency compensation factorbased on the piecewise linear approximation and the digitalrepresentation of the operating temperature; and, a phase-locked loop(PLL) circuit comprising a divider configured to be responsive to thecontrol signal to synthesize the desired frequency; wherein theanalog-to-digital converter is configured to develop the digitalrepresentation of the operating temperature within an accuracy of 0.1 C.17. The device of claim 16, wherein the piecewise linear approximationis further based on an initial frequency offset of the MEMS resonatorfrom the desired frequency.
 18. A device to generate an output signalhaving a desired frequency in connection with a MEMS resonator, thedevice comprising: an analog-to-digital converter to develop a digitalrepresentation of an operating temperature for the MEMS resonator; acontroller to generate a control signal based on the digitalrepresentation of the operating temperature the controller comprising amemory and control logic, wherein the memory stores data comprisingmultiple slope quantities for a piecewise linear approximation of acomposite frequency compensation factor, and wherein the control logicis configured to determine the composite frequency compensation factorbased on the piecewise linear approximation and the digitalrepresentation of the operating temperature; and, a phase-locked loop(PLL) circuit comprising a divider configured to be responsive to thecontrol signal to synthesize the desired frequency; wherein theanalog-to-digital converter is configured such that the digitalrepresentation has a resolution of at least 11 bits.
 19. A method offrequency compensation for a desired output frequency in connection witha MEMS resonator, the method comprising the steps of: receiving aresonator signal from the MEMS resonator; providing an analogtemperature signal indicative of an operating temperature for the MEMSresonator; converting the analog temperature signal into a digitalrepresentation of the operating temperature having a resolution of atleast 11 bits; determining a composite frequency compensation parameterin accordance with the digital representation of the operatingtemperature and the desired output frequency; and, generating an outputsignal having the desired output frequency using a frequency synthesizerbased on the composite frequency compensation parameter.
 20. The methodof claim 19, wherein the determining step comprises calculating thecomposite frequency compensation parameter based on a piecewise linearfunction of the digital representation of the operating temperature.